Escape the Library

【Endless Staircase-02】

At 8:00 in the morning, the course examination of "Endless Ladder" officially started.

Yue Xingwen only felt that it was dark in front of him, and when he regained his vision again, he found that everyone was inside a building.

There is a 45-degree sloping staircase in front. The end of the staircase is connected to the next staircase. All staircases form a "back"-shaped hollow structure. Looking up, you can see the transparent glass skylight at the top of the building.

The floating frame swiped the course prompt: "The exam begins, please go to the rooftop of the building within an hour."

In other words, this labyrinth is made up of countless stairs, as long as you climb the stairs to the top roof, you will complete the test. It sounds very simple, can't you get out when you climb all the way up? However, this class is a maze class in the School of Architecture and certainly no easier than the maze of prime numbers in the School of Mathematics!

The complexity of the maze in the School of Mathematics lies in the operation of prime numbers. Just looking at the internal structure of the maze, there are only three layers: the upper, middle and lower layers. As long as you walk and draw pictures, you can always get out.

However, it is not known how many floors the building of the School of Architecture has. Yue Xingwen didn't dare to be careless. He looked at his teammates and said, "The three-dimensional maze, I don't know how many stairs there are. Don't scatter first. If the maze changes dynamically, you can't find it if you get scattered."

Zhang Xiaonian looked up at the glass ceiling, and took out the laser range finder to measure it. The floor height of this building reached 30 meters. According to the calculation of the first floor of the usual building of 2 meters, 5 to 3 meters, the whole building should be in Between 10 and 15 floors.

The interior of the building is very similar to a common shopping mall. When people look up on the first floor, they can see the glass shed on the roof. The hollow part of the "back" shape is often used to hang holiday balloons and various events. The advertisement of the escalator is inclined upward, from the first floor to the top floor, it is very intuitive at first glance.

Where they are now, they can directly see the rooftop of the building.

However, the 3-credit course of the School of Architecture cannot allow them to climb a few floors and go out like a shopping mall. There must be some mystery inside.

Yue Xingwen looked back at Zhang Xiaonian: "Xiao Nian, can you see what's wrong with this staircase?"

Zhang Xiaonian shook his head: "I can't tell at the moment. The interior design of this building is nothing special. It's exactly the same as the usual shopping malls. We have to walk two floors to see if there is something wrong?"

Yue Xingwen simply said: "Let's go, try climbing a floor first, Ke Shao pays attention to modeling, and measuring distances in small years."

Ke Shaobin immediately took out his laptop, created a new document, and let Xiaotu take pictures and draw the stairs.

Yue Xingwen reminded: "Everyone follow closely, I, Pingce and Xiaonian are in a group of 3, and the remaining 4 people are in a group, and the distance between each other should not be more than 1 step, so as to avoid the stairs suddenly breaking or changing direction. "

Stairs suddenly change direction? This is impossible in reality.

But the library is a magical university. Who knows if this building will suddenly become Harry Potter's castle, walking, and the stairs are broken in the middle, or change in one direction? There is nothing wrong with Yue Xingwen being cautious.

The 7 people were divided into two groups according to the instructions of Yue Xingwen, and the front feet followed by the back feet climbed up.

They quickly climbed the first floor, Jiang Pingce said: "There are 13 steps to the first floor."

Zhang Xiaonian said: "The floor height is 2 meters 5, and the inclination angle is 45 degrees."

Ke Shaobin quickly entered the data in the computer, built the model, and said, "There are 13 steps on the first floor. Where are we on the second floor?"

Zhuo Feng said, "Would you like to make a mark on the stairs to avoid confusion later?"

Yue Xingwen said: "Senior brother, is there a way to mark it?"

Zhuo Feng raised his right hand slightly, and suddenly a golden electric current appeared in his hand, and the electric current shot out with a "Zizi" sound. He controlled the golden electric current, like a golden leather whip in his hand. When the electric current touched the stairs, Zhuo Feng wrote a "1" with his finger, and the golden electric current also followed his finger movement, burning out a charred "1" on the stairs.

Then, he burned out a "2" on the stairs on the next floor.

Everyone: "…"

The marks burned with electric current cannot be wiped off.

Yue Xingwen didn't know whether to laugh or cry: "Can your electricity still be used like this?"

Zhuo Feng withdrew his hand and coughed lightly, "The enhanced electricity can burn anything."

Yue Xingwen praised: "With the mark of senior brother, we will not be in chaos, everyone will continue to follow."

After walking the second floor, Jiang Pingce reported the data: "The second floor is also 13 steps."

Zhang Xiaonian said: "The data is the same as before."

Yue Xingwen said: "Continue."

Everyone followed Yue Xingwen and walked quickly to the third floor.

Jiang Pingce frowned slightly: "It's still the same as before."

Zhuo Feng used electricity to burn a black "3" on the steps, representing the third floor.

Yue Xingwen was puzzled: "The exact same steps, keep going up? The School of Architecture is not so boring, right? Let's continue to climb up to see."

After everyone finished the fourth floor, Jiang Pingce said, "13 steps."

Ke Shaobin entered the data, and then, everyone followed Yue Xingwen around the corner, and when they continued to go up, they were shocked to find that a charred "1" appeared on the stairs ahead.

Everyone looked at each other: "What's the situation?"

Lin Manluo looked at Zhuo Feng suspiciously: "Isn't this the trace you burned on the first floor just now?"

Zhuo Feng was also a little confused: "We obviously climbed up the 4th floor, why did we return to the 1st floor?!"

Yue Xingwen couldn't figure it out either. They had been climbing the stairs just now, and they had climbed 4 floors in a row. As a result, the number "1" appeared in front of them. This is the trace that Brother Zhuo burned on the first floor. Everyone Can never be wrong.

Obviously going up, how come back to the 1st floor?

Jiang Pingce raised his head and glanced at the glass window on the roof, frowning slightly: "After climbing the 4th floor and returning to the 1st floor, we will continue to climb up, and we will return to the 1st floor, repeating the cycle, and we will never get out."

Yue Xingwen said: "Check it out, Senior Brother Zhuo, wait there, Qin Lu, come with me and set a position here. If it's not right, Qin Lu can still come back with plate movement."

Qin Lu nodded and followed Yue Xingwen.

The two quickly climbed up, and after climbing four floors in a row…

Sure enough, he joined a few teammates.

Looking at Yue Xingwen and Qin Lu, who clearly climbed up the stairs from the front, and appeared behind them not long after, everyone looked at each other in dismay. Qin Lu said in a low voice, "Turn around and return to the place, isn't this the same as the ghost hitting the wall in a horror movie?"

Ke Shaobin helped his glasses and said, "In horror movies, the protagonist is often trapped in the stairs at night, desperately running up or down, and as a result, he ran several floors in a row and returned to the starting point..." He nervously Looking at Yue Xingwen, "Did we also encounter ghosts hitting the wall? Can we never get out?"

Yue Xingwen looked back at Zhang Xiaonian, who was staring at Ke Shaobin's laptop in deep thought. Following his gaze, it happened to be a three-dimensional figure modeled by Ke Shaobin in the computer.

Since Zhang Xiaonian measured the data when everyone climbed up just now, the three-dimensional map drawn by Ke Shaobin is very similar to the stairs that everyone sees, and it is almost restored in equal proportions. It can be found from the three-dimensional diagram that the angle between the first floor and the second floor is 90 degrees; between the second floor and the third floor, the third floor and the fourth floor are also vertical angles of 90 degrees.

Seeing the seriousness of the younger brother, Yue Xingwen couldn't help but ask softly, "Xiao Nian, did you find anything?"

Zhang Xiaonian returned to his senses and pointed to the modeling graph: "Assuming that the front is the north, the stairs on the first floor are from west to east, the second floor is from east to south, the third floor is from south to west, and the fourth floor is from west to north. , just to form a ring structure."

Jiang Pingce took a closer look, and it was true.

The direction of the stairs they walked is exactly →, ↓, ←, ↑, forming a ring structure.

Zhang Xiaonian confirmed: "This should be the Penrose Stairs."

Zhuo Feng raised his eyebrows in confusion: "Penrose Stairs? What do you mean?"

Zhang Xiaonian stretched out a hand and made a simple gesture in the air: "In the three-dimensional space, we have been walking upwards, and it is impossible to go up four floors in a row and return to the first floor. But if this is not a three-dimensional space , the twisted space connects the tail of the fourth floor with the starting point of the first floor, which will form a closed and three-dimensional 'back'-shaped stairway. No matter how many times we walk, we will always be on this back-shaped staircase Spin inside."

Jiang Pingce suddenly said: "Similar to the 'Mobius belt'?"

Others looked at them blankly, these professional terms liberal arts students really do not understand.

Jiang Pingce briefly explained: "The Möbius strip is to twist a piece of paper 180 degrees and connect it end to end. A piece of paper that originally had two sides will become only one curved surface. Suppose, Möbius The belt is enlarged into a building, and we walk forward on this paper belt, no matter how long we walk, we will never be able to get out, it is very similar to the Penrose Stairs mentioned by the younger brother."

Zhang Xiaonian nodded: "Yes, the key to the 'Möbius strip' is to twist the note 180 degrees, but the architecture of the three worlds cannot achieve the twisted staircase, so the 'Penrose Staircase' has always been an unrealistic architecture. Hypothesis. But the space of the library can be distorted, and the first floor and the fourth floor are connected end to end, and there is a closed circular staircase that can’t go out.”

No wonder this class is called "Endless Staircase". It turned out to be a circular ladder design similar to "Ghosts Beating the Wall". They don't say it takes 1 hour to walk out of the maze. Even if they climb here for 10 hours, they will continue to climb back from the 4th floor to the 1st floor. Floor, never ending.

Yue Xingwen rubbed his temples: "How do we get out of a building whose space is distorted?"

Zhang Xiaonian looked tangled: "It won't work to climb the stairs all the time, and it will only turn around on the 4th and 1st floors. To crack the Penrose Staircase, we must find where the distorted part is, and return the space there. "

Jiang Pingce said lightly: "If you disconnect that end-to-end connection point, you can break the closed loop."

Zhuo Feng said: "That is, the connection point between the first floor and the fourth floor?"

Zhang Xiaonian hurriedly shook his head: "Not necessarily, it may be the connection point between the 2nd and 3rd, 3rd and 4th floors that is the distorted part. The four-story stairs are like four independent building blocks, originally four building blocks. Both are going up, but one of the pieces is twisted and connected to the other. Since we cannot see the model from outside the three-dimensional space from God's perspective, which piece is twisted cannot be made hastily. judge."

Zhuo Feng understood: "You mean, the '1' I marked is not necessarily the 1st floor? It is possible that the place where we appeared at the beginning was the 2nd floor or the 3rd floor? Anyway, the stairs to the fourth floor are exactly the same, keep going up. , and connected to each other, where is the first floor and where is the fourth floor, we can't actually confirm, right?"

Zhang Xiaonian said: "That's what it means."

Everyone looked at each other and fell into a daze for a while.

Ke Shaobin carefully looked at the modeling graphics, scratched his head and said: "The four-story stairs are exactly the same, including the angle, the number of steps, and the length data. After the circular connection, it looks like a distorted square."

Yue Xingwen looked at Jiang Pingce: "I really don't understand this, tell me, how can I find an exit?"

Jiang Pingce said decisively: "Xiao Nian, measure the data on each floor of the stairs to see how high the stairs are from the ceiling. Is there any difference?"

Zhang Xiaonian quickly reported the result: "Four-story stairs, the specific ceiling height is exactly the same."

Yue Xingwen said with a headache: "That is to say, we seem to be climbing all the time, but in fact, we have been on the same plane, and the height has not changed?"

Zhang Xiaonian nodded: "This is the strange thing about the 'Penrose Staircase', it seems to be going up all the time, but it is actually spinning in the same plane. Three-dimensional space cannot explain such a phenomenon, only higher dimensions are possible. appear."

Jiang Pingce said: "The four floors are the same, so we can only try one by one."

Zhang Xiaonian summoned the excavator.

Everyone: "..."

So, did you use an excavator to get to the maze this time?

Zhang Xiaonian looked at the team leader inquiringly: "Senior brother, did I break the connection?"

Yue Xingwen helped his forehead helplessly: "Okay, let's dig."